{"paper":{"title":"Laurent phenomenon and simple modules of quiver Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Masaki Kashiwara, MyungHo Kim","submitted_at":"2018-11-06T09:13:29Z","abstract_excerpt":"We study consequences of a monoidal categorification of the unipotent quantum coordinate ring $A_q(\\mathfrak{n}(w))$ together with the Laurent phenomenon of cluster algebras. We show that if a simple module $S$ in the category $\\mathcal C_w$ strongly commutes with all the cluster variables in a cluster $[ \\mathscr C]$, then $[S]$ is a cluster monomial in $[ \\mathscr C ]$. If $S$ strongly commutes with cluster variables except exactly one cluster variable $[M_k]$, then $[S]$ is either a cluster monomial in $[\\mathscr C ]$ or a cluster monomial in $\\mu_k([ \\mathscr C ])$. We give a new proof of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02237","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}